Generalizing Bagarello's operator approach to solve a class of partial differential equations
2015
The non-commutative strategy developed by Bagarello (see Int. Jour. of Theoretical Physics, 43, issue 12 (2004), p. 2371 - 2394) for the analysis of systems of ordinary differential equations (ODEs) is extended to a class of partial differential equations (PDEs), namely evolution equations and Navier-Stokes equations. Systems of PDEs are solved using an unbounded self-adjoint, densely defined, Hamiltonian operator and a recursion relation which provides a multiple commutator and a power series solution. Numerous examples are given in this work.
Keywords:
- Distributed parameter system
- Stochastic partial differential equation
- Mathematical analysis
- Semi-elliptic operator
- Separable partial differential equation
- Symbol of a differential operator
- Examples of differential equations
- C0-semigroup
- Discrete mathematics
- Numerical partial differential equations
- Mathematics
- Delay differential equation
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
4
References
0
Citations
NaN
KQI